Abstract
Tom Sederberg's method of moving curves (surfaces) is a new and effective tool for implicitizing curves (surfaces). From our point of view, the curve (surface) can be defined by using moving curves (surfaces) which in algebraic geometry are called correspondences. It turns out that from this definition we can easily derive both parametric and implicit representations of the curve (surface). In this paper, we investigate the geometry of the bi-degree (2,1)-Bezier surface and study the relationship between singularities and correspondences. We also characterize all the possible singular curves in terms of the control points of the surface.
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